What is the direction of the gravitational force
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All bodies attract each other because of their mass. This process is called gravity. The following applies to two bodies: The gravitational force is proportional to the masses of the two bodies and inversely proportional to the square of the distance between the two bodies (whereby the bodies are initially idealized here as point-shaped). The gravitational force that acts on one of the bodies points in the direction of the other. The constant of proportionality is called the constant of gravity and has the value.
In everyday life we experience a special case of these gravitational forces: the force of gravity. It affects every body and is also known as the weight of the body. For the sake of simplicity, let us imagine that the entire mass of the earth is united in its center. In the law of gravitation we combine the earth's mass, the distance from the center to the surface of the earth and the gravitational constant to form a new constant. Then we get for the gravitational force on a body of mass:
is the so-called acceleration due to gravity on the earth's surface. The law of gravity also applies in this form to the less strong simplification of the earth as a sphere with homogeneous mass distribution.
- Example task
Calculate the value of the acceleration due to gravity with a mean equatorial radius of the earth of and the earth's mass of (assuming a mean density):
Name several reasons why the acceleration due to gravity is not a constant!
- According to the law of gravitation, the gravitational pull decreases with increasing distance from the center of the earth. Since the earth is not circular, the acceleration due to gravity is not the same everywhere.
- The mass of the earth is not united in its center, but is distributed over its entire volume. Since the earth is not a homogeneous sphere, but has an inhomogeneous mass distribution (e.g. mountains, seas), the mass attraction can vary depending on the location.
- Part of the gravitational force is needed to keep the body on its orbit. It is also often said: because of the rotation of the earth, centrifugal forces act on a body on its surface. This is described in more detail in the chapters on rotary motion and apparent forces. The resulting attractive force depends on the latitude and is less at the equator than at the poles.
However, these effects are comparatively small, so that they can often be neglected. You then calculate with a mean value of and choose the direction from the center of the earth.
What weight acts on a physics book on mass? What is the acceleration of the book in the earth's gravitational field?
This means: The acceleration due to gravity is the same for all bodies at a certain distance from the center of the earth - regardless of their mass.
- Inertial and heavy mass
In the previous example, the gravity of a body and the acceleration effect of the force were considered and it was assumed that the mass has the same amount in both laws.
The mass is also known as "heavy mass" and is the mass that is involved in gravity.
The mass is called "inertial mass" and is the mass that is accelerated. For example, two bodies with the same carrier mass - one made of iron, the other made of styrofoam - experience the same acceleration with the same force.
So we have two apparently completely different processes, gravitation and acceleration, which follow equivalent laws. In fact, according to the current state of knowledge, there is no difference between inertial mass and heavy mass, i.e. the following applies:
- Inclined plane
The aim is to determine the acceleration of a body of mass that slides smoothly down an inclined plane that is inclined by the angle to the horizontal.
Since the inclined plane forces a certain direction on the body, the acting forces are broken down into components perpendicular and tangential to the plane direction. The vertical component is referred to as the normal force and the tangential component as the downhill force.
The forces acting in this example are the weight of the body, which points downwards, as well as a compensation force from the inclined plane. If only the weight would act, then the body would fall down.
The decomposition of the weight gives the amount of normal force and the amount of downhill force:
Here is the mass of the body and the acceleration due to gravity.
As in the "table and stone" example, the normal force is compensated to zero by the inclined plane, so that the body does not move in a direction perpendicular to the plane. The downhill force accelerates the body downwards along the plane. The following applies to the amount of downhill force:
And for the amount of acceleration:
For is because the plane is then horizontal.
For is because the plane is then vertical and the body falls freely downwards.
The situation with friction is discussed in the following chapter.
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